Novel pulse generator for ultra-wide-band modulating systems and modulating systems using it

ABSTRACT

A pulse generator circuit is provided. The pulse generator circuit has an input adapted to receive an input electrical quantity and an output at which an output electrical quantity is made available. A transfer characteristic establishes a relationship between said input and said output electrical quantities. The pulse generator circuit is adapted to provide said output electrical quantity in the form of pulses having a predetermined shape, suitable to be used for UWB transmission. The transfer characteristic has substantially a same shape as that of said pulses. Moreover, a UWB modulating system exploiting the novel pulse generator is proposed.

TECHNICAL FIELD

The present invention relates to the radio communications field. Morespecifically, the present invention relates to the Ultra-Wide Band (UWB)radio communications field, and in particular it relates to thegeneration of UWB electromagnetic pulses.

BACKGROUND

UWB refers to a radio communications technique fundamentally differentfrom all the other radio frequency communications systems, referred toas “narrowband systems”. Without entering into excessive details, wellknown to those skilled in the art, modulated low-energy pulses of veryshort duration, typically less than one nanosecond are used to transmitdata, whereby the occupied bandwidth has very broad values. According toa definition of the U.S. Federal Communications Commission (FCC), a UWBsystem is a radio system having a bandwidth greater than 20% of thecenter frequency measured at the −10 dB points, or, alternatively,having an RF bandwidth greater than 500 MHz. On Feb. 14, 2002, the FCCallocated limited use of spectrum between the interval 3.1-10.6 GHz forsignals operating in UWB systems (in short, UWB signals).

The main concern regarding a UWB system is that it occupies a portion ofspectrum wherein other narrowband systems already operate, so aregulation is necessary in order to avoid coexistence (e.g.,interference) problems. Therefore, a regulatory authority like the FCChas to set strict limitations in the maximum emission for UWB signals,thus guaranteeing protection to the already existing and deployed radioservices. UWB signal transmissions, following the FCC rules, must have apower spectral density below the involuntary electromagnetic emissionlevel.

A UWB transmitter has to generate UWB pulse signals whose spectrum iscompatible with the regulations, both in term of the frequency intervaland of the maximum emission.

U.S. Pat. No. 6,515,622 discloses an antenna system making use of UWBpulse signals, and describes a technique for generating them based onstep recovery diodes. However, this technique is not compatible withintegrated circuit architectures, and is not adapted to control theshape of the generated pulse signals.

A typical category of UWB pulse signals that are compatible with theregulatory prescriptions of the national/supernational authorities andthat can be easily varied in shape consists of the family of themonocycle wavelets. A Gaussian monocycle wavelet is a short-durationwave having, in the time domain, a shape represented by a Gaussianderivative.

A first solution known in the art for generating a monocycle wavelet isdescribed by H. Kim, D. Park and Joo Y., in “Design of CMOS Shotlz'sMonocycle pulse generator”, IEEE 7803-8187-4 2003, p. 81. According tothis solution, a monocycle wavelet of the second order (i.e.,corresponding to the second time derivative of a Gaussian pulse) isgenerated by differentiating a signal having the shape of a hyperbolictangent by means of a squarer circuit connected to a high-pass filter.However, this solution is adapted to low-frequency applications only.Moreover, since the generated monocycle wavelet is of the second order,its spectrum does not properly match with the spectral interval allowedby the FCC, unless a further filtering operation is performed. However,the further filtering operation increases the pulse duration, resultingin a degradation of the transmission.

An alternative solution for generating a monocycle wavelet is describedby J. F. M. Gerrits and Farserotu, in “Wavelet generation circuit forUWB impulse radio applications”, Electronics Letters, 5 Dec. 2002, Vol.38 n. 25, p. 1737. The document describes a circuit capable ofapproximating a monocycle wavelet of the second order by means of sumsand differences of signals with the shape of a hyperbolic tangent. Thissolution has substantially the same drawbacks as the previous solution.

Another technique for obtaining a monocycle wavelet, or at least toobtain an approximate version thereof, consists of modulating asinusoidal signal (the “carrier signal”) with a modulating signal pulseof suitable shape (in the time domain), thereby obtaining a modulatedsinusoidal carrier monocycle with envelope corresponding to the shape ofthe modulating signal pulse. An advantageous method for obtaining amonocycle wavelet having a spectra suitable for a UWB transmission undere.g. the FCC rules, consists of using modulating signal pulses havingthe shape that is as close as possible to a Gaussian.

I. Gresham and A. Jenkins describe in “A Fast Switching, High IsolationAbsorptive SPST SiGe Switch for 24 GHz Automotive Applications”, 33rdEuropean Microwave Conference, Munich 2003, pag. 903-906, a UWB pulsegenerator circuit that generates a square-envelope modulated monocycleby multiplying a high frequency sinusoidal wave by a square modulatingpulse. This circuit includes a switch circuit having a very shortswitching time, being based on the E²CL architecture. Although thiscircuit is adapted to operate at high frequencies, the spectrum of asquare-envelope modulated monocycle can not be entirely confined in thespectral interval allowed by the FCC, because it is characterized byhaving (ideally infinite) lateral lobes.

The International Application WO 0139451 describes a UWB datatransmission system that generates low level voltage pulses. The shapeof the low level voltage pulses can be varied by means of an adjustableshaping filter. Once shaped, the voltage pulses are used for modulatinga sinusoidal signal, in such a way to obtain the UWB pulse signalsnecessary for the transmission of data. This solution allowsmodification to some extent the shape of the low level voltage pulses,and consequently modifying the shape of the UWB pulse signals spectrum.However, the shaping capability given by the shaping filter is limited,and the spectrum is scarcely controllable, which is also worsened by thecircuit complexity of the shaping filter itself.

SUMMARY

An aspect of the present invention provides a pulse generator circuit.The pulse generator circuit has an input adapted to receive an inputelectrical quantity and an output at which an output electrical quantityis made available. A transfer characteristic establishes a relationshipbetween said input and said output electrical quantities. The pulsegenerator circuit is adapted to provide said output electrical quantityin the form of pulses having a predetermined shape, suitable to be usedfor UWB transmission. The transfer characteristic has substantially asame shape as that of said pulses.

Another aspect of the present invention relates to a UWB modulatingsystem for modulating at least one carrier signal with predeterminedduration enveloping pulses. The UWB modulating system includes a carriergenerator adapted to generate the at least one carrier signal at arespective frequency, a pulse generator circuit for generating saidenveloping pulses having a predetermined shape, suitable to be used forUWB transmission, and a multiplier circuit adapted to multiply the atleast one carrier signal with said enveloping pulses. The pulsegenerator circuit includes an input adapted to receive an inputelectrical quantity, an output at which an output electrical quantity ismade available in form of said enveloping pulses and a transfercharacteristic establishing a relationship between said input and saidoutput electrical quantities. The transfer characteristic hassubstantially a same shape as that of said pulses. The UWB modulatingsystem further includes a driver circuit adapted to generate the inputelectrical quantity fed to the input of the pulse generator circuit.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a UWB transmitter according to anembodiment of the invention;

FIG. 2A is a diagram illustrating characteristics of a UWB signal pulsedepending on time;

FIG. 2B is a diagram illustrating spectral characteristics of a UWBsignal pulse depending on the frequency;

FIG. 3A is a circuit diagram of a UWB pulser according to an embodimentof the present invention;

FIGS. 3B-3D are circuit diagrams illustrating a bias network for biasingthe UWB pulser according to different and alternative embodiments of thepresent invention;

FIGS. 3E-3H are circuit diagrams of the UWB pulser according todifferent and alternative embodiments of the present invention;

FIGS. 4A-4D are diagrams showing the behavior of a circuit having atransfer characteristic with a nearly Gaussian shape;

FIG. 5 is a block diagram of a driver circuit block included in the UWBtransmitter according to an embodiment of the invention; and

FIG. 6 is an exemplary diagram showing waveforms of the signals involvedin the functioning of the driver circuit shown in FIG. 5.

DETAILED DESCRIPTION

The following discussion is presented to enable a person skilled in theart to make and use the invention. Various modifications to theembodiments will be readily apparent to those skilled in the art, andthe generic principles herein may be applied to other embodiments andapplications without departing from the spirit and scope of the presentinvention. Thus, the present invention is not intended to be limited tothe embodiments shown, but is to be accorded the widest scope consistentwith the principles and features disclosed herein.

Referring to FIG. 1, a UWB modulating system, in particular a UWBtransmitter 100, is schematically illustrated according to an embodimentof the present invention. Adopting a Pulse Position Modulation (PPM)technique, the UWB transmitter 100 is adapted to receive a data stream,for example in the form of a modulated digital signal SB carrying astream of bits b_(i), generated by a binary source included in a controlblock 105, and to generate a corresponding train of modulated UWB pulsesignals. Each bit b_(i) can take a high logic value “1” (for example,associated to the value of a supply voltage Vcc), and a low logic value“0” (for example, associated with a ground voltage GND). The train ofmodulated UWB pulse signals, conveying the information carried by thedata stream, i.e. by the modulated digital signal SB, is thenradio-transmitted by means of an antenna 110. The correlation betweenbit values b_(i) and UWB pulse signals is established by the modulationtechnique that is adopted for modulating the digital signal SB.According to the PPM technique, the position of the generic UWB pulsesignal depends on the value, “1” or “0”, of the corresponding bit b_(i)in the data stream. Adopting instead a Pulse Amplitude Modulation (PAM)technique, it is the amplitude of the generic UWB pulse signal thatdepends on the value assumed by the corresponding bit b_(i).

The UWB transmitter 100 includes a UWB pulser 115, having a first inputterminal connected to an output terminal of a driver circuit block 120fed by the modulated digital signal SB, a second input terminalconnected to an output terminal of a sine wave generator block 125, andan output terminal connected to an input terminal of an output stagecircuit 130, having an output terminal connected to the antenna 110. Thedriver circuit block 120 and the sine wave generator block 125 haveinput terminals connected to the control block 105.

When the UWB transmitter 100 has to transmit information, the drivercircuit block 120 receives the data stream, i.e., the digital signal SBmodulated adopting, for example, a PPM technique, and generates acorresponding signal adapted to drive the UWB pulser 115. In particular,the driver circuit block 120 generates a corresponding square wavesignal RP. Moreover, the sine wave generator block 125 generates asinusoidal signal Sc of frequency fc; preferably, the sine wavegenerator block 125 is adapted to generate a sine wave voltage signalhaving a frequency fc variable (in a continuous or discrete way) withina predetermined frequency range, the frequency value being for exampleestablished by the control block 105. The UWB pulser 115 includes apulse generator 140, controlled by the driver circuit block 120, andadapted to generate a signal pulse of carefully selected shape, forexample a nearly-Gaussian pulse Ig, as will be more clear in thefollowing description. The UWB pulser 115 further includes a signalmultiplier block 150, having a first input terminal connected to theoutput terminal of the sine waves generator block 125 for receiving thesinusoidal signal Sc, and a second input terminal connected to the pulsegenerator 140 for receiving the nearly-Gaussian pulse Ig. The multiplierblock 150 further includes an output terminal for providing a UWB signalpulse Pv, given by the product of the sinusoidal signal Sc by thenearly-Gaussian pulse Ig. An output stage circuit 130 allows couplingthe output of the UWB pulser 115 with the antenna 110, without degradingthe spectra of the UWB signal pulse Pv.

Alternatively, a Binary Phase Shift Keying modulation (BPSK) techniquemay be adopted: the data stream is provided to the sine wave generatorblock 125 in the form of a modulated digital signal SB′ carrying astream of bits b′_(i), and the sine wave generator block 125 is drivenby the control block 105 in such a way to modify the phase of thesinusoidal signal Sc depending on the values assumed by the bit b′_(i)of the modulated digital signal SB′.

The qualitative trend of a UWB signal pulse Pv generated by the UWBpulser 115 as a function of time is illustrated in FIG. 2A. The UWBsignal pulse is composed by a sinusoidal wave of frequency fc envelopedby a nearly-Gaussian pulse, and lasts some nanoseconds (being itsbandwidth higher than 500 MHz). As known in the art, the spectrum of asinusoidal wave enveloped by a Gaussian pulse is a Gaussian pulse too,having a center frequency (i.e., the frequency corresponding to themaximum amplitude of the Gaussian pulse) that corresponds to thefrequency of the sinusoidal wave; neglecting the low-amplitude, sideportions of the Gaussian spectrum, the spectral width of the resultingsignal can be considered as confined.

Similarly, the spectrum of the sinusoidal wave signal enveloped by thenearly-Gaussian pulse is given by the spectrum of the nearly-Gaussianpulse, shifted in frequency and centered at the frequency of thesinusoidal wave signal, as illustrated in FIG. 2B; the closer thenearly-Gaussian pulse resemble a Gaussian pulse, the more the spectrumPf of the UWB signal pulse Pv is Gaussian. FIG. 2B shows a diagram ofthe power spectral density of the spectrum Pf versus frequency. Sincethe duration in time of the UWB signal pulse Pv is less than onenanosecond, the spectrum Pf has a corresponding width of several GHz.For being compatible with the FCC rules, the spectrum Pf has to berestricted within a spectral mask SM that begins at the frequency of 3.1GHz and ends at the frequency of 10.6 GHz. Moreover, within thisspectral mask, the power spectral density must have a higher limit valueequal to −41 dBm/MHz.

By acting on the sine waves generator block 125, the control block 105is capable to vary the frequency fc, shifting the entire spectrum Pf.

In a preferred embodiment of the present invention, the shape of thenearly-Gaussian pulse Ig (i.e., the UWB signal pulse envelope) can bevaried, so as to adjust the shape of the spectrum Pf. In particular,according to an embodiment of the present invention, by properlymodifying the square wave signal RP the shape of the nearly-Gaussianpulse Ig can be varied; to this end, the control block 105 acts (controlline 170) on the driver circuit block 120 so as to modify the squarewave signal RP.

The Applicant has found that for generating a pulse of a predeterminedshape, an advantageous solution consists of properly stimulating theinput of a circuit having a non-linear transfer characteristic, whichshape closely approximates, as far as possible, the shape of the desiredpulse. For this reason, in order to generate a nearly Gaussian pulse itis expedient to exploit a circuit whose transfer characteristic has ashape that approximates a Gaussian.

For better understanding the previous statements, reference will be nowmade to FIGS. 4A-4D, wherein the behavior of a circuit having a transfercharacteristic y=NG(x) (x represents a generic input of the circuit, andy a generic output thereof) with a nearly Gaussian shape is analyzed. Ascan be seen in FIG. 4A, the nearly Gaussian shape of the transfercharacteristic y=NG(x) is obtained by the overlap of two non-lineartransfer characteristics, each one having the shape of a hyperbolictangent:

y=NG(x)=A(tan h(x+w)−tan h(x−w)),  (1)

where A is an amplitude parameter and w is a width parameter.

The amplitude parameter A establishes the amplitude of the transfercharacteristic y=NG(x). The width parameter w establishes the shape andthe width of the transfer characteristic y=NG(x), as illustrated in FIG.4B, wherein a family of transfer characteristics y=NG(x) is depicted,depending on different values of the width parameter w: the higher thevalue of the width parameter w, the wider the shape of the transfercharacteristic y=NG(x).

Turning now to FIG. 4C, the effects of an input x variation on theoutput y are illustrated according to a first example, where it isassumed that the input x varies depending on time t x=x(t)) within aninterval of values Δx. According to this first example, the input x(t)is a periodic generically rectangular signal of frequency 1/T between alower value xl and a higher value xh, wherein the difference between thehigher value xh and the lower value xl is equal to the interval Δx.Moreover, the input x(t) has a rise time Tr (i.e., the time it takes forx(t) to rise from xl to xh) equal to the fall time Tf (i.e., the time ittakes for x(t) to fall from xh to xl).

The output y varies over time, i.e. y=y(t), and is in particular aperiodic signal having a period T/2 (i.e., half the period of the inputx(t)). The output y(t) consists of a train of nearly Gaussian pulseseach having the same shape as the transfer characteristic y=NG(x), but,in general, a different duration. More particularly, the output y(t)comprises nearly Gaussian pulses in correspondence of the rising andfalling edges of the input x(t); said nearly Gaussian pulses thus have,a time duration equal to the rise/fall times Tr/Tf. By varying,particularly increasing the rise/fall times Tr/Tf, as is illustrated inFIG. 4D, the time durations of the nearly Gaussian pulses of the outputy(t) are accordingly varied, particularly increased.

Referring to FIG. 3A, a detailed circuit diagram of the UWB pulser 115is illustrated. As previously described, the UWB pulser 115 consists ofa pulse generator 140 and a multiplier block 150.

The pulse generator 140 comprises a first and a second NPN differentialpairs, one having the output terminals cross-coupled to the outputterminals of each other. More particularly, the first differential paircomprises two NPN bipolar transistors Q1, Q2, and the seconddifferential pair comprises two NPN bipolar transistors Q3, Q4. Thetransistors Q1 and Q2 have the emitter terminals connected to eachother, and further connected to a first biasing current generator,supplying a continuous current Iee1. The transistors Q3 and Q4 have theemitter terminals connected to each other, and further connected to asecond biasing current generator supplying a continuous current Iee2.The base terminals of the transistors Q1 and Q3 are connected to theoutput terminal of the driver circuit block 120, schematized in thedrawing as a voltage signal generator generating an input voltage signalVin series-connected to a bias voltage generator generating a continuous(DC) voltage Vb; the collector terminal of the transistor Q1 isconnected to the collector terminal of the transistor Q4, forming acircuital node N1. The transistor Q2 has the base terminal connected toa bias voltage generator supplying a second DC voltage Vb1, and thecollector terminal connected to the collector terminal of the transistorQ3, forming a circuital node N2. The base terminal of the transistor Q4is connected to a bias voltage generator generating a third DC voltageVb2.

The multiplier block 150 comprises a third and a fourth NPN differentialpairs coupled to each other. The third differential pair comprises twoNPN bipolar transistors Q5, Q6, and the fourth differential paircomprises two NPN bipolar transistors Q7, Q8. The transistors Q5 and Q6have the emitter terminals connected to each other and further connectedto the circuital node N1; the transistors Q7 and Q8 have the emitterterminals connected to each other and further connected to the circuitalnode N2. Moreover, the base terminal of the transistor Q5 is connectedto the base terminal of the transistor Q8, and the base terminal of thetransistor Q6 is connected to the base terminal of the transistor Q7.Both the third and the fourth differential pairs are driven by thesinusoidal voltage signal Sc, provided by the sine wave generator block125 in a differential way. More particularly, the sinusoidal voltagesignal Sc is applied between the base terminal of the transistor Q5(positive input terminal) and the base terminal of the transistor Q6(negative input terminal). Consequently, the sinusoidal voltage signalSc is also applied between the base terminal of the transistor Q8(positive input terminal) and the base terminal of the transistor Q7(negative input terminal). The transistors Q5 and Q7 have the collectorterminals connected to each other, defining a first output node No1 ofthe UWB pulser 115. In a similar way, the transistors Q6 and Q8 have thecollector terminals one connected to each other, defining a second UWBpulser output node No2.

A current-to-voltage converter 155 is further provided, attached to theoutput nodes No1 and No2, including a first and a second resistors R1and R2, both having a resistance value Rc. The first resistor R1 isconnected between the first output node No1 and a terminal providing thesupply voltage Vcc, the second resistor R2 is connected between thesecond output node No2 and a terminal providing the supply voltage Vcc.

A differential pair of NPN bipolar transistors exhibits a non-lineartransfer characteristic (expressing the differential output current Idas a function of the differential input voltage Vd), having the shape ofa hyperbolic tangent:

$\begin{matrix}{{{Id} = {\alpha \cdot {Ibias} \cdot {\tanh \left( \frac{Vd}{2{Vt}} \right)}}},} & (2)\end{matrix}$

wherein Ibias is the current biasing the differential pair, α is aproportionality parameter including the saturation current of thetransistors, and Vt is the thermal voltage. It is pointed out that forsmall input voltages Vd (in particular, sufficiently smaller than 2Vt),the transfer characteristic (2) is almost linear, while for large valuesof Vd the non-linearities of the NPN bipolar transistors reduce the gainof the differential pair and cause the transfer characteristic to bend,thereby obtaining the hyperbolic tangent shape.

The behavior of the pulse generator 140 of FIG. 3A is adapted togenerate nearly-Gaussian (current) pulses Ig. In fact, taking account ofequation (2) above, defining with Ig1 the current flowing from theemitter terminals of the transistors Q5 and Q6 to the node N1, anddefining with Ig2 the current flowing from the emitter terminals of thetransistors Q7 and Q8 to the node N2, the differential output currentIg=Ig1−Ig2 of the pulse generator 140 is equal to:

$\begin{matrix}\begin{matrix}{{Ig} = {{{Ig}\; 1} - {{Ig}\; 2}}} \\{= \left( {{{Ic}\; 1} + {{Ic}\; 4} - \left( {{{Ic}\; 2} + {{Ic}\; 3}} \right)} \right)} \\{= {{{{Ic}\; 1} - {{Ic}\; 2} - {{Ic}\; 3} + {{Ic}\; 4}} =}} \\{{= {{{\alpha \cdot {Iee}}\; {1 \cdot {\tanh \left( \frac{{{Vid}\; 1},2}{2{Vt}} \right)}}} - {{\alpha \cdot {Iee}}\; {2 \cdot {\tanh \left( \frac{{{Vid}\; 3},4}{2{Vt}} \right)}}}}},}\end{matrix} & (3)\end{matrix}$

wherein Ic1, Ic2, Ic3, Ic4 are the collector currents of the transistorsQ1, Q2, Q3, Q4, respectively. Vid1,2 is the differential input voltageof the first differential pair, and Vid3,4 is the differential inputvoltage of the second differential pair. Since:

Vid1,2=Vin+Vb−Vb1; Vid3,4=Vin+Vb−Vb2,  (4)

wherein the input signal Vin (representing the square wave signal RPgenerated by the driver circuit block 120) is a square wave signal ofperiod T having rise times Tr and fall times Tf, the equation (3)becomes:

$\begin{matrix}{{{Ig} = {{{\alpha \cdot {Iee}}\; {1 \cdot {\tanh \left( \frac{{Vin} + {Vb} - {{Vb}\; 1}}{2{Vt}} \right)}}} - {{\alpha \cdot {Iee}}\; {2 \cdot {\tanh \left( \frac{{Vin} + {Vb} - {{Vb}\; 2}}{2{Vt}} \right)}}}}},} & (5)\end{matrix}$

which resembles equation (1). The value of the width parameter w ofequation (1) depends on how much the biasing of the transistors Q1, Q2,Q3, Q4 unbalances the corresponding two differential pairs. The value ofthe width parameter w is established in equation (5) by properly settingthe voltages Vb, Vb1 and Vb2 according to the following relationships:

$\begin{matrix}{{{\frac{{Vb} - {{Vb}\; 1}}{2{Vt}} = w};}{\frac{{Vb} - {{Vb}\; 2}}{2{Vt}} = {- {w.}}}} & (6)\end{matrix}$

Since equation (5) resembles equation (1), the pulse generator 140 has atransfer characteristic having a nearly Gaussian shape. Thus, the pulsegenerator 140 is adapted to generate a nearly Gaussian pulse.

The multiplier block 150, having a “Gilbert cell” circuitalarchitecture, is characterized by the following transfer characteristic:

$\begin{matrix}{{Pi} = {{{{Io}\; 1} - {{Io}\; 2}} = {\alpha \cdot {Ig} \cdot {{\tanh \left( \frac{Sc}{2{Vt}} \right)}.}}}} & (7)\end{matrix}$

Io1 and Io2 are the output currents of the multiplier block 150, givenby Ic5+Ic7 and Ic6+Ic8, respectively; Ic5, Ic6, Ic7 and Ic8 are thecollector currents of the transistors Q5, Q6, Q7 and Q8, respectively;the differential output current of the multiplier block 150, i.e.,Io1-Io2, corresponds to the UWB (current) signal pulse.

Defining with Vo1 and Vo2 the voltages at the first and second outputnodes No1, No2, respectively, and thanks to the presence of the firstand second resistors R1, R2, the differential output voltage of the UWBpulser 115, taken between the first output node Not (positive terminal)and the second output node No2 (negative terminal) results equal to(supposing that R1=R2=Rc):

Vo1−Vo2=Vcc−Rc·Io1−(Vcc−Rc·I02)=Rc·(Io2−Io1),  (8)

Substituting equation (7) in equation (8), the following relationship isobtained:

$\begin{matrix}{{{{Vo}\; 1} - {{Vo}\; 2}} = {{- \alpha} \cdot {Rc} \cdot {Ig} \cdot {\tanh \left( \frac{Sc}{2{Vt}} \right)}}} & (9)\end{matrix}$

Substituting now equation (5) in equation (9), the previous equationbecomes:

$\begin{matrix}{{{{Vo}\; 1} - {{Vo}\; 2}} = {\alpha^{2} \cdot {Rc} \cdot {\quad{\left\lbrack {{{Iee}\; {2 \cdot {\tanh \left( \frac{{Vin} + {Vb} - {{Vb}\; 2}}{2{Vt}} \right)}}} - {{Iee}\; {1 \cdot {\tanh \left( \frac{{Vin} + {Vb} - {{Vb}\; 1}}{2{Vt}} \right)}}}} \right\rbrack \cdot {\tanh \left( \frac{Sc}{2{Vt}} \right)}}}}} & (10)\end{matrix}$

By imposing Iee1=Iee2=Iee, equation (10) can be rewritten in thefollowing way:

$\begin{matrix}{{{{Vo}\; 1} - {{Vo}\; 2}} = {\alpha^{2} \cdot {Rc} \cdot {Iee} \cdot {\quad{\left\lbrack {{\tanh \left( \frac{{Vin} + {Vb} - {{Vb}\; 2}}{2{Vt}} \right)} - {\tanh \left( \frac{{Vin} + {Vb} - {{Vb}\; 1}}{2{Vt}} \right)}} \right\rbrack \cdot {\tanh \left( \frac{Sc}{2{Vt}} \right)}}}}} & (11)\end{matrix}$

As can be seen observing equation (11), the differential output voltageof the UWB pulser 115 depends both on the input voltage signal Vin(representing the square wave signal RP generated by the driver circuitblock 120) and on the sinusoidal voltage signal Sc.

Moreover, when the sinusoidal voltage signal Sc has a low amplitude,where by “low amplitude” there is intended sufficiently lower than thethermal voltage Vt, the previous equation can be simplified. In fact,assuming that:

Sc=Vm·sin(2π·fc·t),  (12)

where Vm is the amplitude of the voltage signal Sc, and assuming that:

Vm·sin(2π·fc·t)<<2Vt,  (13)

equation (11) can be approximated in the following way:

$\begin{matrix}{{Pv} = {{{{Vo}\; 1} - {{Vo}\; 2}} \cong {\frac{\alpha^{2} \cdot {Rc} \cdot {Iee} \cdot {Vm}}{2{Vt}} \cdot {\quad{{\left\lbrack {{\tanh \left( \frac{{Vin} + {Vb} - {{Vb}\; 2}}{2{Vt}} \right)} - {\tanh \left( \frac{{Vin} + {Vb} - {{Vb}\; 1}}{2{Vt}} \right)}} \right\rbrack \cdot {\sin \left( {2{\pi \cdot {fc} \cdot t}} \right)}},}}}}} & (14)\end{matrix}$

where the differential output voltage Vo1-Vo2 of the UWB pulser 115corresponds to the UWB voltage signal Pulse Pv. In fact, as can be seenby equation (14), the UWB voltage signal pulse Pv generated by the UWBpulser 115 is a sinusoidal wave enveloped by a nearly-Gaussian pulse.

As previously mentioned, for being adapted to be exploited in atransmission system, the UWB voltage signal pulse Pv has to becompatible with the strict limitations imposed by the regulatoryauthorities like the FCC. In this case, the extension of its spectrum Pfhas to be restricted within the spectral mask SM. By neglecting possiblealiasing effects, an approximated expression of the envelope of theFourier transform of the module of the UWB voltage signal pulse Pv is:

$\begin{matrix}{{{\left( {{Pv}} \right)} = {{Pf} \cong {{\frac{Tr}{T} \cdot \frac{\alpha^{2} \cdot {Iee} \cdot {Rc} \cdot {Vm}}{V\; \max}}{\tanh (w)}{\sqrt{\sqrt{2}{\pi \left( {w + \frac{1}{2}} \right)}} \cdot ^{{- \sqrt{2}}{({w + \frac{1}{2}})}{(\frac{\pi \cdot {Tr} \cdot {Vt} \cdot {({f - {fc}})}}{V\; \max})}^{2}}}}}},} & (15)\end{matrix}$

wherein Vmax is the highest voltage that the square wave signal RPassumes.

From the previous equation, an inverse proportionality relation existsbetween the −10 dB (in respect with the frequency fc) band BW of the UWBvoltage signal pulse Pv and the rise times Tr of the input voltagesignal Vin (i.e., the rise time Tr of the rectangular voltage pulses ofthe square wave signal RP):

$\begin{matrix}{{BW} = {\frac{2V\; \max}{\pi \cdot {Vt} \cdot {Tr}} \cdot {\sqrt{\frac{\ln \sqrt{10}}{\sqrt{2}\left( {w + \frac{1}{2}} \right)}}.}}} & (16)\end{matrix}$

By making explicit the depending of Vmax on Tr and w, the followingrelationship is obtained:

$\begin{matrix}{{{BW} = {\frac{2V\; \max}{\pi \cdot {Vt} \cdot {Tr}} \cdot \sqrt{\frac{\ln \sqrt{10}}{\sqrt{2}\left( {w + \frac{1}{2}} \right)}} \cdot {\ln \left( {\frac{b - a}{2} + \sqrt{\left( \frac{b - a}{2} \right)^{2} - 1}} \right)}}},} & (17)\end{matrix}$

wherein:

$\begin{matrix}{{{a = \frac{^{2w} - ^{{- 2}w}}{p \cdot {\tanh (w)}}};}{{b = {^{2w} + ^{{- 2}w}}},}} & (18)\end{matrix}$

with p that is a ratio term determining the value of Vmax that allowsgenerating a Gaussian pulse having a precision p on the side portionsthereof.

In this way, by varying the rise times Tr of the rectangular voltagepulses of the square wave signal RP generated by the driver circuitblock 120, it is possible to vary the bandwidth BW of the UWB voltagesignal pulse Pv in a reliable way.

Referring now to FIG. 3B, an unbalancing circuit for providing the DCVb, Vb1 and Vb2 to the pulse generator 140 in such a way to unbalancethe differential pairs Q1, Q2 and Q3, Q4 according to equation (6) isdepicted. More particularly, the input voltage signal Vin (representingthe square wave signal RP) is provided to the base terminals of thetransistors Q1 and Q3 by means of a first coupling capacitor Cc1, havinga first terminal receiving the input voltage signal Vin and a secondterminal connected both to the base terminal of the transistor Q1 and tothe base terminal of the transistor Q3. A terminal providing the DCvoltage Vb is connected to the second terminal of the first couplingcapacitor Cc1 by means of a biasing resistor Rb. In the same way, aterminal providing the DC voltage Vb1 is connected to the base terminalof the transistor Q2 by means of a further first biasing resistor Rb1,and a terminal providing the DC voltage Vb2 is connected to the baseterminal of the transistor Q4 by means of a further second biasingresistor Rb2. Moreover, a second and a third coupling capacitors Cc2,Cc3 are included. The second coupling capacitor Cc2 has a first terminalconnected to the base terminal of the transistor Q2 and a secondterminal connected to a terminal providing the ground voltage GND; Thethird coupling capacitor has a first terminal connected to the baseterminal of the transistor Q4 and a second terminal connected to aterminal providing the ground voltage GND.

In case the input voltage signal Vin is provided to the to the pulsegenerator 140 in a differential way, as depicted in FIG. 3C, andaccording to an embodiment of the present invention, the unbalancingcircuit is the same as the one depicted in FIG. 3B, but with the secondterminals of the second and third coupling capacitors that are connectedto each other, and with the input voltage signal Vin that is appliedbetween the first terminal of the first coupling capacitor Cc1 (positiveinput terminal) and the second terminals of the second and thirdcoupling capacitors Cc2, Cc3 (negative input terminal).

A further embodiment of the unbalancing circuit is depicted in FIG. 3D,in which, as in the previous case, the input voltage signal Vin isprovided in a differential way. The input voltage Vin is applied betweenthe base terminal of a NPN bipolar transistor Q9 (positive inputterminal) and the base terminal of a further NPN bipolar transistor Q10(negative output terminal). The transistor Q9 has the collector terminalconnected to a terminal providing the supply voltage Vcc and the emitterterminal connected to the first terminal of a biasing resistor Rb3. Thebiasing resistor Rb3 has a second terminal connected to the baseterminals of the transistors Q1 and Q3, forming a circuital node NB1. Afurther biasing resistor Rb4 has a first terminal connected to the nodeNB1, and a second terminal connected to a biasing current generatorproviding a continuous current Iee3. The transistor Q10 has thecollector terminal connected to a terminal providing the supply voltageVcc and the emitter terminal connected to the base terminal of thetransistor Q4, forming a circuital node NB2. A biasing resistor Rb5 hasa first terminal connected to the node NB2, and a second terminalconnected to a first terminal of a further biasing transistor Rb6. Thebiasing resistor Rb6 has the second terminal connected to the baseterminal of the transistor Q2 and to a biasing current generatorproviding a continuous current Iee4. The input signal Vin is provided tothe inputs of the two differential pairs Q1, Q2 and Q3, Q4 by means ofthe transistors Q9 and Q10, acting as emitter followers. The unbalancingof the differential pairs is accomplished by the voltage drops generatedby the passage of the continuous currents Iee3, Iee4 through the biasingresistors.

Although the UWB pulser 115 previously described has been implementedusing NPN bipolar transistors, alternative solutions are possible. Forexample, similar results can be achieved if each transistor Q1-Q8 inFIG. 3A is replaced by a corresponding voltage-controlled currentgenerator G1-G8, as depicted in FIG. 3E. From a practical viewpoint, thevoltage-controlled current generators may be implemented by MOSFETs, asdepicted in FIG. 3F. As can be seen, the circuital architecture is thesame as that illustrated in FIG. 3A, with the NPN bipolar transistorsQ1-Q8 replaced by n-channel MOSFETs M1-M8.

Mixed solutions are also possible: for example, in FIG. 3G the UWBpulser 115 comprises a pulse generator 140 realized with NPN bipolartransistors and a multiplier block 150 realized with MOSFET transistors;in FIG. 3H the UWB pulser 115 comprises a pulse generator 140 realizedwith MOSFET transistors and a multiplier block 150 realized with NPNbipolar transistors.

As previously mentioned, the UWB pulser 115 converts each transition ofthe square wave signal provided to its input into a corresponding UWBvoltage pulse Pv. Moreover, the time duration of the UWB voltage pulsePv is uniquely determined by the duration of the rise/fall times Tr/Tfof the square wave signal. Since the −10 dB bandwidth BW of the UWBvoltage pulse Pv is inversely proportional to the time duration of theUWB voltage pulse Pv, i.e., to Tr or Tf, the performance in terms ofspeed and temporal coherence of the driver circuit block 120 needs to becarefully controlled; in particular, it is to be observed that thecircuit performances are affected by the fabrication process tolerances.

In FIG. 5, the driver circuit block 120 is depicted according to anembodiment of the present invention, in which the duration of therise/fall times Tr/Tf is constant.

The driver circuit block 120 includes a shift-register 510, a summingnetwork 520 and a low-pass filter 530. The shift register 510 is capableto store a number N of bits b_(i). It receives from the control block105 a clock signal clk having a repetition period Tc, necessary fortiming all the operation performed by the driver circuit block 120, andthe modulated digital signal SB. The shift register 510 provides Noutput bits Q1, Q2, . . . , QN carried by corresponding output terminals(for convenience, the bits and the corresponding terminals providingthem are denoted with the same references) connected in sequence to Ninput terminals S1, S2, . . . , SN of the summing network 520.

Data bits b_(i) are fed by the modulated digital signal SB with afrequency 1/T. The shift register 510 is capable to store an ordinatesequence of N bits, and includes N bistable elements (for example,D-latches implemented with E²CL technology) timed by the same clocksignal clk, one bistable element per bit. Moreover, each bistableelement of the shift register 510 is connected to a corresponding one ofthe output terminals Q1, Q2, . . . , QN. The bistable elements areconnected in such a way that the output of a generic bistable element(except the last) is connected to the input of the subsequent bistableelement. The bits stored in the shift register 510 moves from the firstbistable element (having the output connected to the output terminal Q1)to the last bistable element (having the output connected to the outputterminal QN), passing from a generic bistable element to a subsequentone at each half period Tc/2 of the clock signal clk.

Since, according to this example, the shift register 510 is implementedwith E²CL technology, the D-latches included therein have a differentialcircuit structure, and the logic values “1”, “0” are associated with ahigh logic voltage Vh (e.g., equal to 275 mV) and a low logic voltage Vl(e.g., equal to −275 mV), respectively. Consequently, also the modulateddigital signal has to be properly adapted, by means of a voltage shiftercircuit not shown in the Figure, before being provided to the input ofthe shift register 510. In the starting condition, it is supposed thatthe modulated digital signal SB and the output bits Q1, Q2, . . . , QNare at the low logic voltage Vl. When the modulated digital signal SBassumes the high logic voltage Vh during a half period Tc/2, at thesubsequent half period the output bit Q1 assumes the high logic voltageVh (i.e., it assumes the “1” logic value). If the modulated digitalsignal SB is maintained at the high logic voltage Vh for at least N/2periods Tc, the input variation is transferred to all the N outputterminals; consequently, at the end of N/2 periods Tc, all the outputbits Q1, Q2, . . . , QN are at the high logic voltage Vh (i.e. they areall at the “1” logic value).

The summing network 520 includes an output terminal providing a sumsignal SS to the low-pass filter 530. The sum signal SS is an analogvoltage signal which value is proportional to the number of output bitsQ1, Q2, . . . , QN that are at the high logic voltage Vh:

SS=k·(Q1+Q2+ . . . +QN),  (19)

wherein k is a constant parameter. For example, for implementing thefunction expressed in equation (19) a number N of NPN differential pairsconnected to a same pair of resistors can be used. The sum signal SStakes the highest value when all the output bits Q1, Q2, . . . , QN areat the “1” logic value, and is equal to:

SS _(MAX) =k·N·V _(h).  (20)

FIG. 6 illustrates the time trends of all the signals involved in thegeneration of a single rectangular voltage pulse of the square wavesignal RP, in the exemplary case of a 4-bit shift register 510. In thiscase, the sum signal SS is a rectangular voltage pulse havingstaircase-like rising/falling edges with rise/fall times Tr/Tf equal totwo times the period Tc.

The low pass-filter 530 (that will not be described in detail, becausenot relevant to the scope of the present invention) includes an outputterminal, for providing the square wave signal RP to the UWB pulser 115.In fact, by providing the sum signal SS to the low-pass filter 530, therising/falling edges of the rectangular voltage pulse are smoothed, andtheir trends become nearly linear, as required for properly driving theUWB pulser 115.

According to a further embodiment of the present invention, the drivercircuit block 120 is adapted to be controlled by the control block 105in such a way to vary the duration of the rise/fall times Tr/Tf and,consequently, to adjust the width of the UWB voltage pulses Pv. Sincethe sum signal SS is a rectangular voltage pulse having staircase-likerising/falling edges with rise/fall times Tr/Tf that depend on theperiod Tc of the clock signal clk, a method for varying the rise/falltimes Tr/Tf consists of directly adjusting the period Tc.

Moreover, the rising/falling edges of the signal RC may be non linear.In fact, referring back to FIGS. 4C and 4D, and considering again thegeneric input x and the generic output y related by the nearly-Gaussiantransfer characteristic y=NG(x), a non-linear variation of the input xallows to change the shape of the output y(t). Since the shape variationof a pulse in the time domain implies a corresponding shape variation ofits spectrum in the frequency domain, the possibility of having nonlinear rising/falling edges can be very useful for adjusting thespectrum Pf of the UWB voltage pulses Pv in a carefully controlled way.For example, a driver circuit block 120 adapted to generate rectangularvoltage pulses with non linear rising/falling edges can be implementedby means of a multivibrator circuit, or by properly modifying thecontributions of the bits provided by the shift register.

According to a further embodiment of the present invention, the sinewave generator block 125 (FIG. 1) may generate a signal Sc that is thesum of a plurality of (at least two, more generally) P of sinusoidalwaves Sc1, Sc2, . . . ScP, of different frequencies fc1, fc2, . . . ,fcP. In this way, the spectrum of the signal Sc has a correspondingplurality P of harmonics. If the frequencies fc1, fc2, . . . , fcP aresufficiently spaced from each other, the spectrum of the UWB signalpulse Pv consists of P replicas of the spectrum Pf of thenearly-Gaussian pulse Ig, each replica having a center frequency equalto a corresponding one among the frequencies fc1, fc2, . . . , fcP.Conversely, when the frequencies fc1, fc2, . . . , fcP are sufficientlyclose, said P replicas of the spectrum Pf are mutually influenced: theresulting spectrum has a wider width with respect to spectrum Pf of thenearly-Gaussian pulse Ig.

Naturally, in order to satisfy local and specific requirements, a personskilled in the art may apply to the solution described above manymodifications and alterations. Particularly, although the presentinvention has been described with a certain degree of particularity withreference to preferred embodiment(s) thereof, it should be understoodthat various omissions, substitutions and changes in the form anddetails as well as other embodiments are possible; moreover, it isexpressly intended that specific elements and/or method steps describedin connection with any disclosed embodiment of the invention may beincorporated in any other embodiment as a general matter of designchoice.

The UWB transmitter 100 of FIG. 1 may be utilized in a variety ofdifferent types of electronic communications systems such as wirelesscommunications systems contained in a variety of different types ofelectronic devices such as consumer electronic devices like telephonesand portable digital assistants (PDAs).

1.-13. (canceled)
 14. A UWB modulating system for modulating at leastone carrier signal with predetermined duration enveloping pulses, thesystem including: a carrier generator adapted to generate the at leastone carrier signal having at least one respective frequency; a pulsegenerator circuit for generating said enveloping pulses having apredetermined shape, suitable to be used for UWB transmission; and amultiplier circuit adapted to multiply the at least one carrier signalwith said enveloping pulses, the pulse generator circuit including: aninput adapted to receive an input electrical quantity; an output atwhich an output electrical quantity is made available in form of saidenveloping pulses; and a transfer characteristic establishing arelationship between said input and said output electrical quantities,wherein the transfer characteristic has substantially a same shape assaid predetermined shape; the UWB modulating system further including adriver circuit adapted to generate the input electrical quantity fed tothe input of the pulse generator circuit.
 15. The UWB modulating systemof claim 14, wherein the driver circuit is adapted to generate the inputelectrical quantity in the form of a linear ramp signal.
 16. The UWBmodulating system of claim 15, wherein the driver circuit iscontrollable for varying a slope of the linear ramp signal.
 17. The UWBmodulating system of claim 14, wherein said driver circuit is adapted togenerate the input electrical quantity in the form of a non-linearsignal.
 18. The UWB modulating system of claim 14, wherein the pulsegenerator circuit further includes: a first electronic circuit having afirst non-linear transfer characteristic, a second electronic circuithaving a second non-linear transfer characteristic; said first andsecond electronic circuits being coupled one to the other in such a waythat the first non-linear transfer characteristic is combined with thesecond non-linear transfer characteristic to produce the transfercharacteristic of the pulse generator circuit.
 19. The UWB modulatingsystem of claim 18, wherein the transfer characteristic of the pulsegenerator circuit has a generically Gaussian shape.
 20. The UWBmodulating system of claim 19, wherein the first and the secondnon-linear transfer characteristics of the first and the secondelectronic circuits of the pulse generator circuit have each genericallya shape of a hyperbolic tangent.
 21. The UWB modulating system of claim20, wherein: the first electronic circuit has an input adapted toreceive the input electrical quantity and an output adapted to makeavailable a first output electrical quantity, said output firstelectrical quantity being correlated to the input electrical quantity bythe first non-linear transfer characteristic; the second electroniccircuit has an input adapted to receive the input electrical quantityand an output adapted to make available a second output electricalquantity, said second electrical output quantity being correlated to theinput electrical quantity by the second non-linear transfercharacteristic; and the pulse generator circuit further comprises acombination structure adapted to combine the first electrical outputquantity with the second electrical output quantity and to produce as aresult the output electrical quantity of the pulse generator circuit.22. The UWB modulating system of claim 21, wherein the input electricalquantity is an input voltage signal, the output electrical quantity isan output current signal, and the first and second output electricalquantities are a first and second output current signals, respectively.23. The UWB modulating system of claim 22, wherein: the first electroniccircuit includes a first voltage-controlled current generator circuitfor generating the first output current signal depending on the inputvoltage signal; the second electronic circuit includes a secondvoltage-controlled current generator circuit for generating the secondoutput current signal depending on the input voltage signal, and whereinthe combination structure comprises a current signal summation structureadapted to sum the first and second output current signals and toproduce the output current signal.
 24. The UWB modulating system ofclaim 23, wherein: the first voltage-controlled current generatorcircuit includes a first and a second voltage-controlled currentgenerators having each a voltage control signal input adapted to receivethe input voltage signal and generating corresponding first and secondcontrolled currents, respectively, the first output current signal beinga differential current signal equal to the first controlled currentminus the second controlled current; the second voltage-controlledcurrent generator circuit includes a third and a fourthvoltage-controlled current generators having each a voltage controlsignal input adapted to receive the input voltage signal and generatingcorresponding third and fourth controlled currents, respectively, thesecond output current signal being a differential current signal equalto the third controlled current minus the fourth controlled current. 25.The UWB modulating system of claim 24, wherein the output current signalof the pulse generator circuit is a differential current signalcorresponding to: the first controlled current minus the fourthcontrolled current, minus the second controlled current minus the thirdcontrolled current.
 26. The UWB modulating system of claim 25, whereinthe first, second, third and fourth voltage-controlled currentgenerators includes a first, second, third and fourth transistors,respectively, each one including a first, a second and a controlterminals, the voltage between the control terminal and the firstterminal determining the entity of current drained by the secondterminal.
 27. The UWB modulating system of claim 26, wherein the firsttransistor has the first terminal connected to the first terminal of thesecond transistor and the second terminal connected to the secondterminal of the fourth transistor, the second transistor has the secondterminal connected to the second terminal of the third transistor andthe third transistor has the first terminal connected to the firstterminal of the fourth transistor, the input voltage signal beingapplied between the control terminal of the first transistor and thecontrol terminal of the second transistor, and being applied between thecontrol terminal of the third transistor and the control terminal of thefourth transistor.
 28. The UWB modulating system of claim 27, whereineach transistor is a bipolar transistor, with the first terminal that isan emitter terminal, the control terminal that is a base terminal andthe second terminal that is a collector terminal.
 29. The UWB modulatingsystem of claim 28, wherein each transistor is a MOS transistor, withthe first terminal that is a source terminal, the control terminal thatis a gate terminal and the second terminal that is a drain terminal. 30.The UWB modulating system of claim 29, wherein the carrier generator isadapted to generate the at least one carrier signal as a combination ofa plurality of carrier signals of different frequencies. 31.-35.(canceled)
 36. A UWB modulating method for modulating at least onecarrier signal with an enveloping pulse of predetermined shape,comprising: generating the at least one carrier signal; generating theenveloping pulse; and multiplying the at least one carrier signal by theenveloping pulse, wherein said generating the enveloping pulsecomprises: providing a transfer characteristic establishing arelationship between an input electrical quantity and an outputelectrical quantity, said output electrical quantity forming theenveloping pulse, wherein the transfer characteristic has substantiallya same shape as said predetermined shape.
 37. The method of claim 36,wherein the input electrical quantity has the form of a linear rampsignal.
 38. The method of claim 37, wherein the slope of the linear rampsignal is adapted to be varied.
 39. The method of claim 36, wherein saidinput electrical quantity is a non-linear signal.
 40. The method ofclaim 36, further comprising: providing a first non-linear transfercharacteristic; and providing a second non-linear transfercharacteristic, combining the first non-linear transfer characteristicwith the second non-linear transfer characteristic to produce thetransfer characteristic.
 41. The method of claim 40, wherein thetransfer characteristic has a generically Gaussian shape.
 42. The methodof claim 41, wherein the first and the second non-linear transfercharacteristics have each generically a shape of a hyperbolic tangent.43. The method of claim 42, further comprising: generating a firstoutput electrical quantity, said first output electrical quantity beingcorrelated to the input electrical quantity by the first non-lineartransfer characteristic; and generating a second output electricalquantity, said second output electrical quantity being correlated to theinput electrical quantity by the second non-linear transfercharacteristic; combining the first output electrical quantity with thesecond output electrical quantity to produce the output electricalquantity.
 44. The method of claim 43, wherein the at least one carriersignal includes a combination of a plurality of carrier signals atdifferent frequencies. 45.-57. (canceled)
 58. An electronic system,comprising: a transmitter that comprises: a carrier generator adapted togenerate the at least one carrier signal having at least one respectivefrequency; a pulse generator circuit for generating said envelopingpulses having a predetermined shape, suitable to be used for UWBtransmission; and a multiplier circuit adapted to multiply the at leastone carrier signal with said enveloping pulses, the pulse generatorcircuit including: an input adapted to receive an input electricalquantity; an output at which an output electrical quantity is madeavailable in form of said enveloping pulses; and a transfercharacteristic establishing a relationship between said input and saidoutput electrical quantities, wherein the transfer characteristic hassubstantially a same shape as said predetermined shape; the transmitterfurther including a driver circuit adapted to generate the inputelectrical quantity fed to the input of the pulse generator circuit. 59.The electronic system of claim 58, wherein the driver circuit is adaptedto generate the input electrical quantity in the form of a linear rampsignal.
 60. The electronic system of claim 58, wherein the drivercircuit is controllable for varying a slope of the linear ramp signal.61. The electronic system of claim 58, wherein said driver circuit isadapted to generate the input electrical quantity in the form of anon-linear signal.
 62. The electronic system of claim 58, wherein thepulse generator circuit further includes: a first electronic circuithaving a first non-linear transfer characteristic, a second electroniccircuit having a second non-linear transfer characteristic; said firstand second electronic circuits being coupled one to the other in such away that the first non-linear transfer characteristic is combined withthe second non-linear transfer characteristic to produce the transfercharacteristic of the pulse generator circuit.
 63. The electronic systemof claim 62, wherein the transfer characteristic of the pulse generatorcircuit has a generically Gaussian shape.
 64. The electronic system ofclaim 63, wherein the first and the second non-linear transfercharacteristics of the first and the second electronic circuits of thepulse generator circuit have each generically a shape of a hyperbolictangent.